Students' solutions of enumerative combinatorial problems may be assessed along two main dimensions: the correctness of the solution and the method of enumeration. This study looks at the second dimension with reference to the Cartesian product of two sets, and at the 'odometer' combinatorial strategy defined by English (1991). Since we are not…

This paper was inspired by the work of a previous contributor on the subject of modelling plague epidemiology by comparing it to the physics of series radioactive decay, RC transients, and fluid dynamics. An Arduino-based experiment to illustrate the fluid-dynamical case is described. Attention is drawn to important differences between systems…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

The paper discusses some interesting, mainly philosophical paradigms of the modeling and control areas, which are still partly unsolved and/or only partially studied. First the possible introduction of a prejudice free control--similar to the term for the modeling introduced by Rudi Kalman--is investigated. Next the real constraints in real…

Teaching students with Intellectual Disability (ID) is a relatively new endeavor. Beginning in 2001 with the passage of the No Child Left Behind Act, the general education curriculum integrated algebra across the K-12 curriculum (Kendall, 2011; National Governors Association Center for Best Practices & Council of Chief State School Officers,…

We use the Enron email corpus to study relationships in a network by applying six different measures of centrality. Our results came out of an in-semester undergraduate research seminar. The Enron corpus is well suited to statistical analyses at all levels of undergraduate education. Through this article's focus on centrality, students can explore…

The purpose of this article is to present two very active applied modeling projects that were successfully implemented in a first semester calculus course at Hollins University. The first project uses a logistic equation to model the spread of a new disease such as swine flu. The second project is a human take on the popular article "Do Dogs Know…

Behavioral momentum theory provides a quantitative account of how reinforcers experienced within a discriminative stimulus context govern the persistence of behavior that occurs in that context. The theory suggests that all reinforcers obtained in the presence of a discriminative stimulus increase resistance to change, regardless of whether those…

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

In this paper we derive an expression for the dynamic electric polarizability of a particle bound by a double delta potential for frequencies below and above the absolute value of the particle's ground state energy. The derived expression will be used to study some of the fundamental features of the system and its representation of real systems.…

Four empirical laws of bibliometrics--anomalous number, Lotka's, Zipf's, and Bradford's--together with Laplace's "law of succession" and de Solla Price's cumulative advantage distribution are shown to be almost identical. A simple model shows that the frequency forms conform with inverse square law over appropriate interval. (Fifteen…

Defines relationship between user profile and user query in terms of relationship between clusters of documents retrieved by each, and explores the expression of cluster similarity and cluster overlap as linear functions of similarity existing between original pairs of profiles and queries, given the desired retrieval threshold. (23 references)…